Question

A manufacturer of bulbs for movie projectors finds that the lives of the bulbs are normally distributed with a mean of 61 hours and a standard deviation of 6.3 hours. The manufacturer will guarantee the bulbs so that only 3% will be replaced because of failure before the guaranteed number of hours. For how many hours should the bulbs be guaranteed?

Answer 1

49.2 hours

Explanation:

Use a chart or calculator to find the z-score associated with the probability.

P(Z < z) = 0.03

z = -1.88

Now find the x value.

z = (x − μ) / σ

-1.88 = (x − 61) / 6.3

x = 49.2